A Moving Average Bidirectional Texture Function Model

The Bidirectional Texture Function (BTF) is the recent most advanced representation of visual properties of surface materials. It specifies their appearance due to varying spatial, illumination, and viewing conditions. Corresponding enormous BTF measurements require a mathematical representation allowing extreme compression but simultaneously preserving its high visual fidelity. We present a novel BTF model based on a set of underlying mono-spectral two-dimensional (2D) moving average factors. A mono-spectral moving average model assumes that a stochastic mono-spectral texture is produced by convolving an uncorrelated 2D random field with a 2D filter which completely characterizes the
texture. The BTF model combines several multi-spectral band limited spatial factors, subsequently factorized into a set of mono-spectral moving average representations, and range map to produce the required BTF texture space. This enables very high BTF space compression ratio, unlimited texture enlargement, and reconstruction of missing unmeasured parts of the BTF space.

ResultsWe have tested the model on BTF colour textures from the University of Bonn BTF measurements consist of several materials such as wood or leather. Each BTF material sample comprised in the University of Bonn database is measured in 81 illumination and 81 viewing angles and has resolution 800×800 pixels. The resulting texture quality is approaching existing alternative BTF models based on 2D random fields: Causal Auto-Regressive model (CAR2D) and Gaussian Markov random field model (GMRF 2D). BTF moving average model represents a simple alternative to these BTF models. Multispectral (both BTF or non-BTF) models based on spectral factorization (2D random field models) have problems to correctly represent spectrum of motley textures. The MA2D models spectrally outperforms both these alternative models due to its weak spatial correlations. The main advantage of the moving average model is its stability, which is a problem which has to be occasionally treated for CAR models. The GMRF models require approximate parameters estimation and demanding texture synthesis. Another advantage of the model is its numerical efficiency.